complex nrs determine polynomial from zeros of function

Jun 2012
12
0
How do I determine the 4th degree polynomial with real coefficients from the following zeros of that function?
(i) and 2-3i.
 
Jun 2014
945
191
Earth
How do I determine the 4th degree polynomial with real coefficients from the following zeros of that function?
(i) and 2-3i.
You are given the equivalent of:

0 + i \(\displaystyle \ \ \) and

2 - 3i


The other zeroes are their conjugates:

0 - i \(\displaystyle \ \ \) and

2 + 3i


Your corresponding factors are:

x - i

x - (-i) = x + i

x - (2 - 3i)

x + (2 + 3i)


Multiply them together.